TSTP Solution File: NUM412+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : NUM412+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 10:21:58 EDT 2023
% Result : Theorem 1.06s 1.17s
% Output : CNFRefutation 1.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM412+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.11 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.11/0.32 % Computer : n027.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Aug 25 13:52:18 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.16/0.55 start to proof:theBenchmark
% 1.06/1.16 %-------------------------------------------
% 1.06/1.16 % File :CSE---1.6
% 1.06/1.16 % Problem :theBenchmark
% 1.06/1.16 % Transform :cnf
% 1.06/1.16 % Format :tptp:raw
% 1.06/1.16 % Command :java -jar mcs_scs.jar %d %s
% 1.06/1.16
% 1.06/1.16 % Result :Theorem 0.540000s
% 1.06/1.16 % Output :CNFRefutation 0.540000s
% 1.06/1.16 %-------------------------------------------
% 1.06/1.16 %------------------------------------------------------------------------------
% 1.06/1.16 % File : NUM412+1 : TPTP v8.1.2. Released v3.2.0.
% 1.06/1.16 % Domain : Number Theory (Ordinals)
% 1.06/1.16 % Problem : Ordinal numbers, theorem 48
% 1.06/1.16 % Version : [Urb06] axioms : Especial.
% 1.06/1.16 % English :
% 1.06/1.16
% 1.06/1.16 % Refs : [Ban90] Bancerek (1990), The Ordinal Numbers
% 1.06/1.16 % [Urb06] Urban (2006), Email to G. Sutcliffe
% 1.06/1.16 % Source : [Urb06]
% 1.06/1.16 % Names : ordinal1__t48_ordinal1 [Urb06]
% 1.06/1.16
% 1.06/1.16 % Status : Theorem
% 1.06/1.16 % Rating : 0.14 v7.5.0, 0.16 v7.4.0, 0.07 v7.1.0, 0.09 v7.0.0, 0.10 v6.4.0, 0.15 v6.3.0, 0.17 v6.2.0, 0.16 v6.1.0, 0.20 v6.0.0, 0.17 v5.5.0, 0.22 v5.4.0, 0.29 v5.3.0, 0.30 v5.2.0, 0.10 v5.1.0, 0.14 v5.0.0, 0.17 v4.1.0, 0.22 v4.0.1, 0.26 v4.0.0, 0.25 v3.7.0, 0.10 v3.5.0, 0.11 v3.4.0, 0.16 v3.3.0, 0.07 v3.2.0
% 1.06/1.16 % Syntax : Number of formulae : 48 ( 6 unt; 0 def)
% 1.06/1.16 % Number of atoms : 143 ( 3 equ)
% 1.06/1.16 % Maximal formula atoms : 8 ( 2 avg)
% 1.06/1.16 % Number of connectives : 105 ( 10 ~; 1 |; 67 &)
% 1.06/1.16 % ( 2 <=>; 25 =>; 0 <=; 0 <~>)
% 1.06/1.16 % Maximal formula depth : 8 ( 4 avg)
% 1.06/1.16 % Maximal term depth : 2 ( 1 avg)
% 1.06/1.16 % Number of predicates : 16 ( 15 usr; 0 prp; 1-2 aty)
% 1.06/1.16 % Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% 1.06/1.16 % Number of variables : 68 ( 52 !; 16 ?)
% 1.06/1.16 % SPC : FOF_THM_RFO_SEQ
% 1.06/1.16
% 1.06/1.17 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% 1.06/1.17 % library, www.mizar.org
% 1.06/1.17 %------------------------------------------------------------------------------
% 1.06/1.17 fof(antisymmetry_r2_hidden,axiom,
% 1.06/1.17 ! [A,B] :
% 1.06/1.17 ( in(A,B)
% 1.06/1.17 => ~ in(B,A) ) ).
% 1.06/1.17
% 1.06/1.17 fof(cc1_funct_1,axiom,
% 1.06/1.17 ! [A] :
% 1.06/1.17 ( empty(A)
% 1.06/1.17 => function(A) ) ).
% 1.06/1.17
% 1.06/1.17 fof(cc1_ordinal1,axiom,
% 1.06/1.17 ! [A] :
% 1.06/1.17 ( ordinal(A)
% 1.06/1.17 => ( epsilon_transitive(A)
% 1.06/1.17 & epsilon_connected(A) ) ) ).
% 1.06/1.17
% 1.06/1.17 fof(cc1_relat_1,axiom,
% 1.06/1.17 ! [A] :
% 1.06/1.17 ( empty(A)
% 1.06/1.17 => relation(A) ) ).
% 1.06/1.17
% 1.06/1.17 fof(cc2_funct_1,axiom,
% 1.06/1.17 ! [A] :
% 1.06/1.17 ( ( relation(A)
% 1.06/1.17 & empty(A)
% 1.06/1.17 & function(A) )
% 1.06/1.17 => ( relation(A)
% 1.06/1.17 & function(A)
% 1.06/1.17 & one_to_one(A) ) ) ).
% 1.06/1.17
% 1.06/1.17 fof(cc2_ordinal1,axiom,
% 1.06/1.17 ! [A] :
% 1.06/1.17 ( ( epsilon_transitive(A)
% 1.06/1.17 & epsilon_connected(A) )
% 1.06/1.17 => ordinal(A) ) ).
% 1.06/1.17
% 1.06/1.17 fof(cc3_ordinal1,axiom,
% 1.06/1.17 ! [A] :
% 1.06/1.17 ( empty(A)
% 1.06/1.17 => ( epsilon_transitive(A)
% 1.06/1.17 & epsilon_connected(A)
% 1.06/1.17 & ordinal(A) ) ) ).
% 1.06/1.17
% 1.06/1.17 fof(d8_ordinal1,axiom,
% 1.06/1.17 ! [A,B] :
% 1.06/1.17 ( ( relation(B)
% 1.06/1.17 & function(B)
% 1.06/1.17 & transfinite_sequence(B) )
% 1.06/1.17 => ( transfinite_sequence_of(B,A)
% 1.06/1.17 <=> subset(relation_rng(B),A) ) ) ).
% 1.06/1.17
% 1.06/1.17 fof(dt_k2_ordinal1,axiom,
% 1.06/1.17 ! [A,B] :
% 1.06/1.17 ( ( relation(A)
% 1.06/1.17 & function(A)
% 1.06/1.17 & transfinite_sequence(A)
% 1.06/1.17 & ordinal(B) )
% 1.06/1.17 => transfinite_sequence_of(tseq_dom_restriction(A,B),relation_rng(A)) ) ).
% 1.06/1.17
% 1.06/1.17 fof(dt_k7_relat_1,axiom,
% 1.06/1.17 ! [A,B] :
% 1.06/1.17 ( relation(A)
% 1.06/1.17 => relation(relation_dom_restriction(A,B)) ) ).
% 1.06/1.17
% 1.06/1.17 fof(dt_m1_ordinal1,axiom,
% 1.06/1.17 ! [A,B] :
% 1.06/1.17 ( transfinite_sequence_of(B,A)
% 1.06/1.17 => ( relation(B)
% 1.06/1.17 & function(B)
% 1.06/1.17 & transfinite_sequence(B) ) ) ).
% 1.06/1.17
% 1.06/1.17 fof(existence_m1_ordinal1,axiom,
% 1.06/1.17 ! [A] :
% 1.06/1.17 ? [B] : transfinite_sequence_of(B,A) ).
% 1.06/1.17
% 1.06/1.17 fof(existence_m1_subset_1,axiom,
% 1.06/1.17 ! [A] :
% 1.06/1.17 ? [B] : element(B,A) ).
% 1.06/1.17
% 1.06/1.17 fof(fc12_relat_1,axiom,
% 1.06/1.17 ( empty(empty_set)
% 1.06/1.17 & relation(empty_set)
% 1.06/1.17 & relation_empty_yielding(empty_set) ) ).
% 1.06/1.17
% 1.06/1.17 fof(fc13_relat_1,axiom,
% 1.06/1.17 ! [A,B] :
% 1.06/1.17 ( ( relation(A)
% 1.06/1.17 & relation_empty_yielding(A) )
% 1.06/1.17 => ( relation(relation_dom_restriction(A,B))
% 1.06/1.17 & relation_empty_yielding(relation_dom_restriction(A,B)) ) ) ).
% 1.06/1.17
% 1.06/1.17 fof(fc1_xboole_0,axiom,
% 1.06/1.17 empty(empty_set) ).
% 1.06/1.17
% 1.06/1.17 fof(fc2_ordinal1,axiom,
% 1.06/1.17 ( relation(empty_set)
% 1.06/1.17 & relation_empty_yielding(empty_set)
% 1.06/1.17 & function(empty_set)
% 1.06/1.17 & one_to_one(empty_set)
% 1.06/1.17 & empty(empty_set)
% 1.06/1.17 & epsilon_transitive(empty_set)
% 1.06/1.17 & epsilon_connected(empty_set)
% 1.06/1.17 & ordinal(empty_set) ) ).
% 1.06/1.17
% 1.06/1.17 fof(fc4_funct_1,axiom,
% 1.06/1.17 ! [A,B] :
% 1.06/1.17 ( ( relation(A)
% 1.06/1.17 & function(A) )
% 1.06/1.17 => ( relation(relation_dom_restriction(A,B))
% 1.06/1.17 & function(relation_dom_restriction(A,B)) ) ) ).
% 1.06/1.17
% 1.06/1.17 fof(fc4_relat_1,axiom,
% 1.06/1.17 ( empty(empty_set)
% 1.06/1.17 & relation(empty_set) ) ).
% 1.06/1.17
% 1.06/1.17 fof(fc6_funct_1,axiom,
% 1.06/1.17 ! [A] :
% 1.06/1.17 ( ( relation(A)
% 1.06/1.17 & relation_non_empty(A)
% 1.06/1.17 & function(A) )
% 1.06/1.17 => with_non_empty_elements(relation_rng(A)) ) ).
% 1.06/1.17
% 1.06/1.17 fof(fc6_relat_1,axiom,
% 1.06/1.17 ! [A] :
% 1.06/1.17 ( ( ~ empty(A)
% 1.06/1.17 & relation(A) )
% 1.06/1.17 => ~ empty(relation_rng(A)) ) ).
% 1.06/1.17
% 1.06/1.17 fof(fc8_relat_1,axiom,
% 1.06/1.17 ! [A] :
% 1.06/1.17 ( empty(A)
% 1.06/1.17 => ( empty(relation_rng(A))
% 1.06/1.17 & relation(relation_rng(A)) ) ) ).
% 1.06/1.17
% 1.06/1.17 fof(rc1_funct_1,axiom,
% 1.06/1.17 ? [A] :
% 1.06/1.17 ( relation(A)
% 1.06/1.17 & function(A) ) ).
% 1.06/1.17
% 1.06/1.17 fof(rc1_ordinal1,axiom,
% 1.06/1.17 ? [A] :
% 1.06/1.17 ( epsilon_transitive(A)
% 1.06/1.17 & epsilon_connected(A)
% 1.06/1.17 & ordinal(A) ) ).
% 1.06/1.17
% 1.06/1.17 fof(rc1_relat_1,axiom,
% 1.06/1.17 ? [A] :
% 1.06/1.17 ( empty(A)
% 1.06/1.17 & relation(A) ) ).
% 1.06/1.17
% 1.06/1.17 fof(rc1_xboole_0,axiom,
% 1.06/1.17 ? [A] : empty(A) ).
% 1.06/1.17
% 1.06/1.17 fof(rc2_funct_1,axiom,
% 1.06/1.17 ? [A] :
% 1.06/1.17 ( relation(A)
% 1.06/1.17 & empty(A)
% 1.06/1.17 & function(A) ) ).
% 1.06/1.17
% 1.06/1.17 fof(rc2_ordinal1,axiom,
% 1.06/1.17 ? [A] :
% 1.06/1.17 ( relation(A)
% 1.06/1.17 & function(A)
% 1.06/1.17 & one_to_one(A)
% 1.06/1.17 & empty(A)
% 1.06/1.17 & epsilon_transitive(A)
% 1.06/1.17 & epsilon_connected(A)
% 1.06/1.17 & ordinal(A) ) ).
% 1.06/1.17
% 1.06/1.17 fof(rc2_relat_1,axiom,
% 1.06/1.17 ? [A] :
% 1.06/1.17 ( ~ empty(A)
% 1.06/1.17 & relation(A) ) ).
% 1.06/1.17
% 1.06/1.17 fof(rc2_xboole_0,axiom,
% 1.06/1.17 ? [A] : ~ empty(A) ).
% 1.06/1.17
% 1.06/1.17 fof(rc3_funct_1,axiom,
% 1.06/1.17 ? [A] :
% 1.06/1.17 ( relation(A)
% 1.06/1.17 & function(A)
% 1.06/1.17 & one_to_one(A) ) ).
% 1.06/1.17
% 1.06/1.17 fof(rc3_ordinal1,axiom,
% 1.06/1.17 ? [A] :
% 1.06/1.17 ( ~ empty(A)
% 1.06/1.17 & epsilon_transitive(A)
% 1.06/1.17 & epsilon_connected(A)
% 1.06/1.17 & ordinal(A) ) ).
% 1.06/1.17
% 1.06/1.17 fof(rc3_relat_1,axiom,
% 1.06/1.17 ? [A] :
% 1.06/1.17 ( relation(A)
% 1.06/1.17 & relation_empty_yielding(A) ) ).
% 1.06/1.17
% 1.06/1.17 fof(rc4_funct_1,axiom,
% 1.06/1.17 ? [A] :
% 1.06/1.17 ( relation(A)
% 1.06/1.17 & relation_empty_yielding(A)
% 1.06/1.17 & function(A) ) ).
% 1.06/1.17
% 1.06/1.17 fof(rc4_ordinal1,axiom,
% 1.06/1.17 ? [A] :
% 1.06/1.17 ( relation(A)
% 1.06/1.17 & function(A)
% 1.06/1.17 & transfinite_sequence(A) ) ).
% 1.06/1.17
% 1.06/1.17 fof(rc5_funct_1,axiom,
% 1.06/1.17 ? [A] :
% 1.06/1.17 ( relation(A)
% 1.06/1.17 & relation_non_empty(A)
% 1.06/1.17 & function(A) ) ).
% 1.06/1.17
% 1.06/1.17 fof(redefinition_k2_ordinal1,axiom,
% 1.06/1.17 ! [A,B] :
% 1.06/1.17 ( ( relation(A)
% 1.06/1.17 & function(A)
% 1.06/1.17 & transfinite_sequence(A)
% 1.06/1.17 & ordinal(B) )
% 1.06/1.17 => tseq_dom_restriction(A,B) = relation_dom_restriction(A,B) ) ).
% 1.06/1.17
% 1.06/1.17 fof(reflexivity_r1_tarski,axiom,
% 1.06/1.17 ! [A,B] : subset(A,A) ).
% 1.06/1.17
% 1.06/1.17 fof(t1_subset,axiom,
% 1.06/1.17 ! [A,B] :
% 1.06/1.17 ( in(A,B)
% 1.06/1.17 => element(A,B) ) ).
% 1.06/1.17
% 1.06/1.17 fof(t2_subset,axiom,
% 1.06/1.17 ! [A,B] :
% 1.06/1.17 ( element(A,B)
% 1.06/1.17 => ( empty(B)
% 1.06/1.17 | in(A,B) ) ) ).
% 1.06/1.17
% 1.06/1.17 fof(t3_subset,axiom,
% 1.06/1.17 ! [A,B] :
% 1.06/1.17 ( element(A,powerset(B))
% 1.06/1.17 <=> subset(A,B) ) ).
% 1.06/1.17
% 1.06/1.17 fof(t47_ordinal1,axiom,
% 1.06/1.17 ! [A,B] :
% 1.06/1.17 ( subset(A,B)
% 1.06/1.17 => ! [C] :
% 1.06/1.17 ( transfinite_sequence_of(C,A)
% 1.06/1.17 => transfinite_sequence_of(C,B) ) ) ).
% 1.06/1.17
% 1.06/1.17 fof(t48_ordinal1,conjecture,
% 1.06/1.17 ! [A,B] :
% 1.06/1.17 ( transfinite_sequence_of(B,A)
% 1.06/1.17 => ! [C] :
% 1.06/1.17 ( ordinal(C)
% 1.06/1.17 => transfinite_sequence_of(tseq_dom_restriction(B,C),A) ) ) ).
% 1.06/1.17
% 1.06/1.17 fof(t4_subset,axiom,
% 1.06/1.17 ! [A,B,C] :
% 1.06/1.17 ( ( in(A,B)
% 1.06/1.17 & element(B,powerset(C)) )
% 1.06/1.17 => element(A,C) ) ).
% 1.06/1.17
% 1.06/1.17 fof(t5_subset,axiom,
% 1.06/1.17 ! [A,B,C] :
% 1.06/1.17 ~ ( in(A,B)
% 1.06/1.17 & element(B,powerset(C))
% 1.06/1.17 & empty(C) ) ).
% 1.06/1.17
% 1.06/1.17 fof(t6_boole,axiom,
% 1.06/1.17 ! [A] :
% 1.06/1.17 ( empty(A)
% 1.06/1.17 => A = empty_set ) ).
% 1.06/1.17
% 1.06/1.17 fof(t7_boole,axiom,
% 1.06/1.17 ! [A,B] :
% 1.06/1.17 ~ ( in(A,B)
% 1.06/1.17 & empty(B) ) ).
% 1.06/1.17
% 1.06/1.17 fof(t8_boole,axiom,
% 1.06/1.17 ! [A,B] :
% 1.06/1.17 ~ ( empty(A)
% 1.06/1.17 & A != B
% 1.06/1.17 & empty(B) ) ).
% 1.06/1.17
% 1.06/1.17 %------------------------------------------------------------------------------
% 1.06/1.17 %-------------------------------------------
% 1.06/1.17 % Proof found
% 1.06/1.17 % SZS status Theorem for theBenchmark
% 1.06/1.17 % SZS output start Proof
% 1.06/1.17 %ClaNum:125(EqnAxiom:30)
% 1.06/1.17 %VarNum:134(SingletonVarNum:60)
% 1.06/1.17 %MaxLitNum:5
% 1.06/1.17 %MaxfuncDepth:1
% 1.06/1.17 %SharedTerms:69
% 1.06/1.17 %goalClause: 51 82 89
% 1.06/1.17 %singleGoalClaCount:3
% 1.06/1.17 [34]P1(a1)
% 1.06/1.17 [35]P1(a2)
% 1.06/1.17 [36]P1(a17)
% 1.06/1.17 [37]P1(a18)
% 1.06/1.17 [38]P1(a19)
% 1.06/1.17 [39]P3(a1)
% 1.06/1.18 [40]P3(a3)
% 1.06/1.18 [41]P3(a18)
% 1.06/1.18 [42]P3(a19)
% 1.06/1.18 [43]P3(a4)
% 1.06/1.18 [44]P3(a6)
% 1.06/1.18 [45]P3(a9)
% 1.06/1.18 [46]P3(a10)
% 1.06/1.18 [47]P6(a1)
% 1.06/1.18 [48]P6(a16)
% 1.06/1.18 [49]P6(a19)
% 1.06/1.18 [50]P6(a7)
% 1.06/1.18 [51]P6(a11)
% 1.06/1.18 [52]P4(a1)
% 1.06/1.18 [53]P4(a16)
% 1.06/1.18 [54]P4(a19)
% 1.06/1.18 [55]P4(a7)
% 1.06/1.18 [56]P5(a1)
% 1.06/1.18 [57]P5(a16)
% 1.06/1.18 [58]P5(a19)
% 1.06/1.18 [59]P5(a7)
% 1.06/1.18 [62]P9(a1)
% 1.06/1.18 [63]P9(a3)
% 1.06/1.18 [64]P9(a2)
% 1.06/1.18 [65]P9(a18)
% 1.06/1.18 [66]P9(a19)
% 1.06/1.18 [67]P9(a20)
% 1.06/1.18 [68]P9(a4)
% 1.06/1.18 [69]P9(a8)
% 1.06/1.18 [70]P9(a6)
% 1.06/1.18 [71]P9(a9)
% 1.06/1.18 [72]P9(a10)
% 1.06/1.18 [73]P7(a1)
% 1.06/1.18 [74]P7(a19)
% 1.06/1.18 [75]P7(a4)
% 1.06/1.18 [76]P10(a9)
% 1.06/1.18 [78]P11(a1)
% 1.06/1.18 [79]P11(a8)
% 1.06/1.18 [80]P11(a6)
% 1.06/1.18 [81]P12(a10)
% 1.06/1.18 [82]P14(a12,a13)
% 1.06/1.18 [86]~P1(a20)
% 1.06/1.18 [87]~P1(a5)
% 1.06/1.18 [88]~P1(a7)
% 1.06/1.18 [89]~P14(f21(a12,a11),a13)
% 1.06/1.18 [83]P13(x831,x831)
% 1.06/1.18 [84]P14(f14(x841),x841)
% 1.06/1.18 [85]P2(f15(x851),x851)
% 1.06/1.18 [90]~P1(x901)+E(x901,a1)
% 1.06/1.18 [91]~P1(x911)+P3(x911)
% 1.06/1.18 [92]~P1(x921)+P6(x921)
% 1.06/1.18 [93]~P1(x931)+P4(x931)
% 1.06/1.18 [94]~P6(x941)+P4(x941)
% 1.06/1.18 [95]~P1(x951)+P5(x951)
% 1.06/1.18 [96]~P6(x961)+P5(x961)
% 1.06/1.18 [97]~P1(x971)+P9(x971)
% 1.06/1.18 [99]~P1(x991)+P1(f22(x991))
% 1.06/1.18 [100]~P1(x1001)+P9(f22(x1001))
% 1.06/1.18 [103]P3(x1031)+~P14(x1031,x1032)
% 1.06/1.18 [104]P9(x1041)+~P14(x1041,x1042)
% 1.06/1.18 [105]P10(x1051)+~P14(x1051,x1052)
% 1.06/1.18 [107]~P1(x1071)+~P8(x1072,x1071)
% 1.06/1.18 [109]~P8(x1091,x1092)+P2(x1091,x1092)
% 1.06/1.18 [117]~P8(x1172,x1171)+~P8(x1171,x1172)
% 1.06/1.18 [110]~P9(x1101)+P9(f23(x1101,x1102))
% 1.06/1.18 [112]~P13(x1121,x1122)+P2(x1121,f24(x1122))
% 1.06/1.18 [118]P13(x1181,x1182)+~P2(x1181,f24(x1182))
% 1.06/1.18 [101]~P4(x1011)+~P5(x1011)+P6(x1011)
% 1.06/1.18 [106]~P9(x1061)+P1(x1061)+~P1(f22(x1061))
% 1.06/1.18 [98]~P1(x982)+~P1(x981)+E(x981,x982)
% 1.06/1.18 [111]~P2(x1112,x1111)+P1(x1111)+P8(x1112,x1111)
% 1.06/1.18 [113]~P3(x1131)+~P9(x1131)+P3(f23(x1131,x1132))
% 1.06/1.18 [116]~P9(x1161)+~P11(x1161)+P11(f23(x1161,x1162))
% 1.06/1.18 [120]~P13(x1203,x1202)+P14(x1201,x1202)+~P14(x1201,x1203)
% 1.06/1.18 [121]~P1(x1211)+~P8(x1212,x1213)+~P2(x1213,f24(x1211))
% 1.06/1.18 [124]P2(x1241,x1242)+~P8(x1241,x1243)+~P2(x1243,f24(x1242))
% 1.06/1.18 [102]~P1(x1021)+~P3(x1021)+~P9(x1021)+P7(x1021)
% 1.06/1.18 [108]~P3(x1081)+~P9(x1081)+~P12(x1081)+P15(f22(x1081))
% 1.06/1.18 [119]~P3(x1191)+~P6(x1192)+~P9(x1191)+~P10(x1191)+E(f21(x1191,x1192),f23(x1191,x1192))
% 1.06/1.18 [122]~P3(x1221)+~P9(x1221)+~P10(x1221)+~P14(x1221,x1222)+P13(f22(x1221),x1222)
% 1.06/1.18 [123]~P3(x1231)+~P9(x1231)+~P10(x1231)+P14(x1231,x1232)+~P13(f22(x1231),x1232)
% 1.06/1.18 [125]~P3(x1251)+~P6(x1252)+~P9(x1251)+~P10(x1251)+P14(f21(x1251,x1252),f22(x1251))
% 1.06/1.18 %EqnAxiom
% 1.06/1.18 [1]E(x11,x11)
% 1.06/1.18 [2]E(x22,x21)+~E(x21,x22)
% 1.06/1.18 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 1.06/1.18 [4]~E(x41,x42)+E(f14(x41),f14(x42))
% 1.06/1.18 [5]~E(x51,x52)+E(f15(x51),f15(x52))
% 1.06/1.18 [6]~E(x61,x62)+E(f21(x61,x63),f21(x62,x63))
% 1.06/1.18 [7]~E(x71,x72)+E(f21(x73,x71),f21(x73,x72))
% 1.06/1.18 [8]~E(x81,x82)+E(f22(x81),f22(x82))
% 1.06/1.18 [9]~E(x91,x92)+E(f24(x91),f24(x92))
% 1.06/1.18 [10]~E(x101,x102)+E(f23(x101,x103),f23(x102,x103))
% 1.06/1.18 [11]~E(x111,x112)+E(f23(x113,x111),f23(x113,x112))
% 1.06/1.18 [12]~P1(x121)+P1(x122)+~E(x121,x122)
% 1.06/1.18 [13]~P10(x131)+P10(x132)+~E(x131,x132)
% 1.06/1.18 [14]~P9(x141)+P9(x142)+~E(x141,x142)
% 1.06/1.18 [15]~P6(x151)+P6(x152)+~E(x151,x152)
% 1.06/1.18 [16]~P3(x161)+P3(x162)+~E(x161,x162)
% 1.06/1.18 [17]P14(x172,x173)+~E(x171,x172)+~P14(x171,x173)
% 1.06/1.18 [18]P14(x183,x182)+~E(x181,x182)+~P14(x183,x181)
% 1.06/1.18 [19]P2(x192,x193)+~E(x191,x192)+~P2(x191,x193)
% 1.06/1.18 [20]P2(x203,x202)+~E(x201,x202)+~P2(x203,x201)
% 1.06/1.18 [21]P8(x212,x213)+~E(x211,x212)+~P8(x211,x213)
% 1.06/1.18 [22]P8(x223,x222)+~E(x221,x222)+~P8(x223,x221)
% 1.06/1.18 [23]~P5(x231)+P5(x232)+~E(x231,x232)
% 1.06/1.18 [24]~P4(x241)+P4(x242)+~E(x241,x242)
% 1.06/1.18 [25]~P7(x251)+P7(x252)+~E(x251,x252)
% 1.06/1.18 [26]P13(x262,x263)+~E(x261,x262)+~P13(x261,x263)
% 1.06/1.18 [27]P13(x273,x272)+~E(x271,x272)+~P13(x273,x271)
% 1.06/1.18 [28]~P11(x281)+P11(x282)+~E(x281,x282)
% 1.06/1.18 [29]~P15(x291)+P15(x292)+~E(x291,x292)
% 1.06/1.18 [30]~P12(x301)+P12(x302)+~E(x301,x302)
% 1.06/1.18
% 1.06/1.18 %-------------------------------------------
% 1.06/1.18 cnf(126,plain,
% 1.06/1.18 (~P8(x1261,a1)),
% 1.06/1.18 inference(scs_inference,[],[34,107])).
% 1.06/1.18 cnf(127,plain,
% 1.06/1.18 (P13(f15(f24(x1271)),x1271)),
% 1.06/1.18 inference(scs_inference,[],[34,85,107,118])).
% 1.06/1.18 cnf(128,plain,
% 1.06/1.18 (P2(f15(x1281),x1281)),
% 1.06/1.18 inference(rename_variables,[],[85])).
% 1.06/1.18 cnf(131,plain,
% 1.06/1.18 (P8(f15(a20),a20)),
% 1.06/1.18 inference(scs_inference,[],[82,34,86,89,85,128,107,118,17,111])).
% 1.06/1.18 cnf(132,plain,
% 1.06/1.18 (P2(f15(x1321),x1321)),
% 1.06/1.18 inference(rename_variables,[],[85])).
% 1.06/1.18 cnf(134,plain,
% 1.06/1.18 (~P8(x1341,f15(f24(a1)))),
% 1.06/1.18 inference(scs_inference,[],[82,34,86,89,85,128,132,107,118,17,111,121])).
% 1.06/1.18 cnf(140,plain,
% 1.06/1.18 (~P8(a20,f15(a20))),
% 1.06/1.18 inference(scs_inference,[],[82,34,37,41,65,86,89,85,128,132,107,118,17,111,121,102,2,117])).
% 1.06/1.18 cnf(142,plain,
% 1.06/1.18 (P10(a12)),
% 1.06/1.18 inference(scs_inference,[],[82,34,37,41,65,86,89,85,128,132,107,118,17,111,121,102,2,117,105])).
% 1.06/1.18 cnf(144,plain,
% 1.06/1.18 (P9(a12)),
% 1.06/1.18 inference(scs_inference,[],[82,34,37,41,65,86,89,85,128,132,107,118,17,111,121,102,2,117,105,104])).
% 1.06/1.18 cnf(146,plain,
% 1.06/1.18 (P3(a12)),
% 1.06/1.18 inference(scs_inference,[],[82,34,37,41,65,86,89,85,128,132,107,118,17,111,121,102,2,117,105,104,103])).
% 1.06/1.18 cnf(160,plain,
% 1.06/1.18 (P3(a2)),
% 1.06/1.18 inference(scs_inference,[],[51,82,34,35,36,37,41,65,86,89,85,128,132,107,118,17,111,121,102,2,117,105,104,103,97,96,95,94,93,92,91])).
% 1.06/1.18 cnf(166,plain,
% 1.06/1.18 (P9(f23(a1,x1661))),
% 1.06/1.18 inference(scs_inference,[],[51,83,82,34,35,36,37,41,62,65,86,89,85,128,132,107,118,17,111,121,102,2,117,105,104,103,97,96,95,94,93,92,91,90,112,110])).
% 1.06/1.18 cnf(172,plain,
% 1.06/1.18 (E(f23(x1721,a2),f23(x1721,a1))),
% 1.06/1.18 inference(scs_inference,[],[51,83,82,34,35,36,37,41,62,65,86,89,85,128,132,107,118,17,111,121,102,2,117,105,104,103,97,96,95,94,93,92,91,90,112,110,100,99,11])).
% 1.06/1.18 cnf(173,plain,
% 1.06/1.18 (E(f23(a2,x1731),f23(a1,x1731))),
% 1.06/1.18 inference(scs_inference,[],[51,83,82,34,35,36,37,41,62,65,86,89,85,128,132,107,118,17,111,121,102,2,117,105,104,103,97,96,95,94,93,92,91,90,112,110,100,99,11,10])).
% 1.06/1.18 cnf(185,plain,
% 1.06/1.18 (P11(f23(a1,x1851))),
% 1.06/1.18 inference(scs_inference,[],[51,83,82,34,35,36,37,41,62,65,78,81,86,89,85,128,132,107,118,17,111,121,102,2,117,105,104,103,97,96,95,94,93,92,91,90,112,110,100,99,11,10,9,8,7,6,5,4,30,22,12,120,116])).
% 1.06/1.18 cnf(187,plain,
% 1.06/1.18 (P3(f23(a1,x1871))),
% 1.06/1.18 inference(scs_inference,[],[51,83,82,34,35,36,37,39,41,62,65,78,81,86,89,85,128,132,107,118,17,111,121,102,2,117,105,104,103,97,96,95,94,93,92,91,90,112,110,100,99,11,10,9,8,7,6,5,4,30,22,12,120,116,113])).
% 1.06/1.18 cnf(189,plain,
% 1.06/1.18 (~P1(f22(a20))),
% 1.06/1.18 inference(scs_inference,[],[51,83,82,34,35,36,37,39,41,62,65,67,78,81,86,89,85,128,132,107,118,17,111,121,102,2,117,105,104,103,97,96,95,94,93,92,91,90,112,110,100,99,11,10,9,8,7,6,5,4,30,22,12,120,116,113,106])).
% 1.06/1.18 cnf(201,plain,
% 1.06/1.18 (~P13(x2011,a2)+~E(a10,a1)+P13(x2011,a1)),
% 1.06/1.18 inference(scs_inference,[],[51,83,82,34,35,36,37,39,41,45,62,65,67,71,76,78,81,86,89,85,128,132,107,118,17,111,121,102,2,117,105,104,103,97,96,95,94,93,92,91,90,112,110,100,99,11,10,9,8,7,6,5,4,30,22,12,120,116,113,106,108,123,122,125,119,27])).
% 1.06/1.18 cnf(213,plain,
% 1.06/1.18 (P13(f22(a12),a13)),
% 1.06/1.18 inference(scs_inference,[],[82,142,144,146,122])).
% 1.06/1.18 cnf(222,plain,
% 1.06/1.18 (P13(x2221,x2221)),
% 1.06/1.18 inference(rename_variables,[],[83])).
% 1.06/1.18 cnf(224,plain,
% 1.06/1.18 (P13(x2241,x2241)),
% 1.06/1.18 inference(rename_variables,[],[83])).
% 1.06/1.18 cnf(225,plain,
% 1.06/1.18 (~E(f15(f24(a19)),a20)),
% 1.06/1.18 inference(scs_inference,[],[51,38,85,83,222,45,76,71,82,131,142,144,146,122,121,119,112,27,26,19])).
% 1.06/1.18 cnf(226,plain,
% 1.06/1.18 (P2(f15(x2261),x2261)),
% 1.06/1.18 inference(rename_variables,[],[85])).
% 1.06/1.18 cnf(228,plain,
% 1.06/1.18 (P14(f14(x2281),x2281)),
% 1.06/1.18 inference(rename_variables,[],[84])).
% 1.06/1.18 cnf(233,plain,
% 1.06/1.18 (E(f23(x2331,a2),f23(x2331,a1))),
% 1.06/1.18 inference(rename_variables,[],[172])).
% 1.06/1.18 cnf(235,plain,
% 1.06/1.18 (P1(f15(f24(a1)))),
% 1.06/1.18 inference(scs_inference,[],[51,38,87,84,228,85,226,89,83,222,45,76,71,82,134,172,173,131,142,144,146,122,121,119,112,27,26,19,18,17,12,3,111])).
% 1.06/1.18 cnf(249,plain,
% 1.06/1.18 (E(f23(x2491,a1),f23(x2491,a2))),
% 1.06/1.18 inference(scs_inference,[],[51,38,40,46,63,69,72,79,87,64,81,84,228,85,226,89,83,222,224,45,76,71,82,35,134,172,233,173,131,142,144,146,160,122,121,119,112,27,26,19,18,17,12,3,111,116,113,108,123,125,102,2])).
% 1.06/1.18 cnf(258,plain,
% 1.06/1.18 (E(f21(a9,a1),f23(a9,a1))),
% 1.06/1.18 inference(scs_inference,[],[47,45,76,71,119])).
% 1.06/1.18 cnf(263,plain,
% 1.06/1.18 (P14(f21(a9,a1),f22(a9))),
% 1.06/1.18 inference(scs_inference,[],[47,83,45,76,71,142,144,146,119,123,125])).
% 1.06/1.18 cnf(281,plain,
% 1.06/1.18 (P14(f21(a9,a16),f22(a9))),
% 1.06/1.18 inference(scs_inference,[],[48,45,76,71,125])).
% 1.06/1.18 cnf(283,plain,
% 1.06/1.18 (E(f21(a9,a16),f23(a9,a16))),
% 1.06/1.18 inference(scs_inference,[],[48,45,76,71,125,119])).
% 1.06/1.18 cnf(288,plain,
% 1.06/1.18 (E(f21(a9,a1),f23(a9,a2))),
% 1.06/1.18 inference(scs_inference,[],[48,88,36,84,45,76,71,258,249,125,119,18,12,3])).
% 1.06/1.18 cnf(293,plain,
% 1.06/1.18 (E(f23(a9,a1),f21(a9,a1))),
% 1.06/1.18 inference(scs_inference,[],[48,88,36,84,45,76,71,263,258,249,134,131,125,119,18,12,3,17,22,2])).
% 1.06/1.18 cnf(295,plain,
% 1.06/1.18 (P8(f15(a7),a7)),
% 1.06/1.18 inference(scs_inference,[],[48,88,36,84,85,45,76,71,140,263,258,249,134,131,125,119,18,12,3,17,22,2,21,111])).
% 1.06/1.18 cnf(309,plain,
% 1.06/1.18 (P14(f14(x3091),x3091)),
% 1.06/1.18 inference(rename_variables,[],[84])).
% 1.06/1.18 cnf(312,plain,
% 1.06/1.18 (~E(a18,a5)),
% 1.06/1.18 inference(scs_inference,[],[87,37,84,288,293,172,18,3,12])).
% 1.06/1.18 cnf(314,plain,
% 1.06/1.18 (~E(a7,a1)),
% 1.06/1.18 inference(scs_inference,[],[87,126,37,84,225,288,293,295,172,18,3,12,2,22])).
% 1.06/1.18 cnf(317,plain,
% 1.06/1.18 (P9(f14(x3171))),
% 1.06/1.18 inference(scs_inference,[],[87,126,37,84,309,76,225,288,293,295,172,18,3,12,2,22,13,104])).
% 1.06/1.18 cnf(319,plain,
% 1.06/1.18 (P3(f14(x3191))),
% 1.06/1.18 inference(scs_inference,[],[87,126,37,84,309,76,225,288,293,295,172,18,3,12,2,22,13,104,103])).
% 1.06/1.18 cnf(329,plain,
% 1.06/1.18 (P10(f14(x3291))),
% 1.06/1.18 inference(scs_inference,[],[68,87,126,37,84,309,76,225,288,293,295,172,18,3,12,2,22,13,104,103,110,92,93,99,105])).
% 1.06/1.18 cnf(339,plain,
% 1.06/1.18 (E(a18,a1)),
% 1.06/1.18 inference(scs_inference,[],[68,87,126,37,36,84,309,76,225,288,293,295,235,172,18,3,12,2,22,13,104,103,110,92,93,99,105,100,97,95,91,90])).
% 1.06/1.18 cnf(341,plain,
% 1.06/1.18 (E(f23(a18,x3411),f23(a1,x3411))),
% 1.06/1.18 inference(scs_inference,[],[68,87,126,37,36,84,309,76,225,288,293,295,235,172,18,3,12,2,22,13,104,103,110,92,93,99,105,100,97,95,91,90,10])).
% 1.06/1.18 cnf(356,plain,
% 1.06/1.18 (E(f23(x3561,a18),f23(x3561,a1))),
% 1.06/1.18 inference(scs_inference,[],[339,11])).
% 1.06/1.18 cnf(358,plain,
% 1.06/1.18 (E(f15(a18),f15(a1))),
% 1.06/1.18 inference(scs_inference,[],[339,11,6,5])).
% 1.06/1.18 cnf(360,plain,
% 1.06/1.18 (E(f24(a18),f24(a1))),
% 1.06/1.18 inference(scs_inference,[],[339,11,6,5,4,9])).
% 1.06/1.18 cnf(363,plain,
% 1.06/1.18 (E(f23(a1,x3631),f23(a18,x3631))),
% 1.06/1.18 inference(scs_inference,[],[126,341,312,339,11,6,5,4,9,3,22,2])).
% 1.06/1.18 cnf(365,plain,
% 1.06/1.18 (P13(f15(f24(x3651)),x3651)),
% 1.06/1.18 inference(rename_variables,[],[127])).
% 1.06/1.18 cnf(373,plain,
% 1.06/1.18 (P13(f15(f24(a18)),a1)),
% 1.06/1.18 inference(scs_inference,[],[127,365,44,70,80,126,38,85,341,312,339,11,6,5,4,9,3,22,2,201,116,121,113,27])).
% 1.06/1.18 cnf(401,plain,
% 1.06/1.18 (E(f23(a1,x4011),f23(a18,x4011))),
% 1.06/1.18 inference(rename_variables,[],[363])).
% 1.06/1.18 cnf(403,plain,
% 1.06/1.18 (E(f23(a1,x4031),f23(a18,x4031))),
% 1.06/1.18 inference(rename_variables,[],[363])).
% 1.06/1.18 cnf(404,plain,
% 1.06/1.18 (P9(f21(a9,a16))),
% 1.06/1.18 inference(scs_inference,[],[363,401,281,166,187,16,14,104])).
% 1.06/1.18 cnf(409,plain,
% 1.06/1.18 (~P2(a7,f24(a1))),
% 1.06/1.18 inference(scs_inference,[],[34,363,401,185,281,166,187,295,16,14,104,116,121])).
% 1.06/1.18 cnf(411,plain,
% 1.06/1.18 (~P13(a7,a1)),
% 1.06/1.18 inference(scs_inference,[],[34,363,401,185,281,166,187,295,16,14,104,116,121,112])).
% 1.06/1.18 cnf(415,plain,
% 1.06/1.18 (E(a19,a1)),
% 1.06/1.18 inference(scs_inference,[],[34,43,68,38,363,401,185,281,166,187,295,16,14,104,116,121,112,113,90])).
% 1.06/1.18 cnf(419,plain,
% 1.06/1.18 (P2(f15(x4191),x4191)),
% 1.06/1.18 inference(rename_variables,[],[85])).
% 1.06/1.18 cnf(420,plain,
% 1.06/1.18 (P8(f15(a5),a5)),
% 1.06/1.18 inference(scs_inference,[],[34,43,68,87,38,85,419,356,363,401,373,185,281,166,187,295,16,14,104,116,121,112,113,90,26,20,111])).
% 1.06/1.18 cnf(426,plain,
% 1.06/1.18 (E(f23(a1,a18),f23(a18,a1))),
% 1.06/1.18 inference(scs_inference,[],[34,43,68,88,87,38,85,419,84,356,363,401,403,373,185,281,166,187,295,16,14,104,116,121,112,113,90,26,20,111,18,12,3])).
% 1.06/1.18 cnf(477,plain,
% 1.06/1.18 (~P14(f21(a12,a11),f22(a12))),
% 1.06/1.18 inference(scs_inference,[],[34,50,52,127,126,85,83,84,71,45,76,409,404,426,420,411,415,314,358,360,283,189,329,317,319,185,281,213,373,89,14,123,112,27,26,19,20,18,12,3,22,17,2,24,118,28,125,119,120])).
% 1.06/1.18 cnf(605,plain,
% 1.06/1.18 ($false),
% 1.06/1.18 inference(scs_inference,[],[477,142,144,146,51,125]),
% 1.06/1.18 ['proof']).
% 1.06/1.18 % SZS output end Proof
% 1.06/1.18 % Total time :0.540000s
%------------------------------------------------------------------------------